In strictly mathematical terms, the image produced or black and white film is one dimensional (brightness), while an original scene can be viewed as three dimensional (using the HLS model of color, where hue, luminance, and saturation are the dimensions). The chemical reaction of the film emulsion, and the camera mechanisms and filters, essentially reduce the three dimensional information to one dimension by complex mapping, and forever obliterate the original hue, luminance, and saturation information.
Note: It should be pointed out that luminance and brightness are not the same. Since brightness of the black and white image results from the complex interactions of the three elements of the HLS system, there is only a statistical correlation between brightness and luminance, but they are not identical.